{"title":"解决卢卡，梅纳雷斯和皮萨罗-马达里亚加的问题","authors":"Yuchen Ding, Lilu Zhao","doi":"10.4064/aa230604-12-7","DOIUrl":null,"url":null,"abstract":"Let $k\\ge 2$ be a positive integer and $P^+(n)$ the greatest prime factor of a positive integer $n$ with convention $P^+(1)=1$. For any $\\theta \\in \\left [\\frac 1{2k},\\frac {17}{32k}\\right )$, set $$T_{k,\\theta }(x)=\\sum _{\\substack {p_1\\cdot \\cdot \\c","PeriodicalId":37888,"journal":{"name":"Acta Arithmetica","volume":"70 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solution to a problem of Luca, Menares and Pizarro-Madariaga\",\"authors\":\"Yuchen Ding, Lilu Zhao\",\"doi\":\"10.4064/aa230604-12-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $k\\\\ge 2$ be a positive integer and $P^+(n)$ the greatest prime factor of a positive integer $n$ with convention $P^+(1)=1$. For any $\\\\theta \\\\in \\\\left [\\\\frac 1{2k},\\\\frac {17}{32k}\\\\right )$, set $$T_{k,\\\\theta }(x)=\\\\sum _{\\\\substack {p_1\\\\cdot \\\\cdot \\\\c\",\"PeriodicalId\":37888,\"journal\":{\"name\":\"Acta Arithmetica\",\"volume\":\"70 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Arithmetica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4064/aa230604-12-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Arithmetica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/aa230604-12-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Solution to a problem of Luca, Menares and Pizarro-Madariaga
Let $k\ge 2$ be a positive integer and $P^+(n)$ the greatest prime factor of a positive integer $n$ with convention $P^+(1)=1$. For any $\theta \in \left [\frac 1{2k},\frac {17}{32k}\right )$, set $$T_{k,\theta }(x)=\sum _{\substack {p_1\cdot \cdot \c
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